Solve the problem. Show your work. Responses will be graded using the short-response scoring rubric given at the beginning of the lesson.

A passing boat is 310 feet from the base of a lighthouse. The angle of depression from the top of the lighthouse is 24°. What is the height of the lighthouse to the nearest tenth of a foot?

The equation that models the cost x in dollars of a single phone is given by 293.75 ≤ x ≤ 306.25.

What are inequalities ?

When two values are compared , an inequality represents whether one is greater than, less than, or not equal to the other.

It is given that total cost of phone is $25 above or below $1200.

This is a case of inequality.

Let's assume the cost of one phone is $x.

So cost of 4 phones will be given by 4x.

and this will be equal to total cost which is given as $25 above or below $1200.

So , the inequality is given by ;

1200 - 25 ≤ 4x ≤ 1200 + 25

1175 ≤ 4x ≤ 1225

If we divide by 4 through this inequality then ;

(1175/4) ≤ (4x/ 4) ≤ (1225/ 4)

or

293.75 ≤ x ≤ 306.25

The cost of one phone will lie between $293.75 and $306.25.

Therefore , the equation that models the cost x in dollars of a single phone is given by 293.75 ≤ x ≤ 306.25.

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By interpreting the equation of the circle in standard form, we conclude that the circle (x + 4)² + (y - 6)² = 48 has a radius of approximately 6.928 units.

In this question we find the equation of a circle in standard form, whose expression is described and explained below:

(x - h)² + (y - k)² = r²

Where:

According to the equation given in the statement, we find a circle with a center at (- 4, 6) and a radius of 6.928 units.

By interpreting the equation of the circle in standard form, we conclude that the circle (x + 4)² + (y - 6)² = 48 has a radius of approximately 6.928 units.

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The function rule for the direct variation in the table is [tex]y = 24/x[/tex] , indirect variation ; x = 2.4.

Direct variation is the change in one quantity as a result of the change in another. This suggests that if one quantity rises or falls, the other must rise or fall correspondingly as well.

The formula y = kx is used to answer direct variation questions. If finding the proportionality constant is necessary, the answer is obtained by dividing y by x.

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The missing measure to the nearest hundredth is  r = 2.25 in, C = 14.13 in.

A circle's outside boundary is called the circumference and can be measured, or calculated, by using

Circumference = 2πr

where r is the radius of circle.

Now it is given that,

Diameter of circle, d = 8 1/2 in = 9/2 in

So, radius of circle, r = d/2 = 9/4 in

⇒ r = 2.25 in

Therefore,

∵ Circumference of circle, C = 2πr

∴ Circumference of circle, C = 2π*9/4

⇒ Circumference of circle, C = 14.130 in

Thus, the missing measure to the nearest hundredth is r = 2.25 in, C = 14.13 in.

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Step-by-step explanation:

The answer is 99+(77+88)

From the given linear functions, the ordered pairs that represents a function is A= {(-6, 6),(-3, 2),(0, -1) (3, 5})

A set of ordered equation represents a linear function if the domain of the coordinates are not repeated.

For instance, the ordered pairs that is a function are the coordinates that do not have any repeated x-coordinates.

From the given linear functions, the ordered pairs that represents a function is A= {(-6, 6),(-3, 2),(0, -1) (3, 5})

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The equivalent expression of the given expression is (x^3y + 5xy^2)/6

The expression is given as:

(1)/(6)x^(3)y+(5)/(6)xy^(2)

Rewrite properly as

1/6x^3y + 5/6xy^2

Take the LCM

So, we have

(x^3y + 5xy^2)/6

Hence, the equivalent expression of the given expression is (x^3y + 5xy^2)/6

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Answer:

See the attached photos for help!

Step-by-step explanation:

I also recommend looking up desmos graphing calculator to actually see the graphs!

If you need more in depth assistance on this, feel free to let me know :]

Answer: x= -1

Step-by-step explanation:

[tex]3\left|2x+2\right|-2x=x+3\\[/tex]

Next, we find Positive and Negative Intervals!

[tex]x < -1,\:\:x\ge \:-1[/tex]

Then Last we Solve The inequality for each interval.

No Solution or x= -1

Answer: I got my answer by dividing 14 by 35, then multiplying by 100.

Answer: 250 minutes.

Step-by-step explanation: You make a fraction.

Actual time / Percentage

Then you multiply that by 100.

The final coordinates of the triangle are A''(x, y) = (3, 2), B''(x, y) = (- 1, 4) and C''(x, y) = (2, 0), respectively.

In this question we know the coordinates of the three vertices of the triangle, whose image must be generated by combining reflection across y-axis and translation, two kinds of rigid transformations, whose formulas are summarized below:

Reflection across y-axis

P'(x, y) = P(x, y) + (- 2 · p, 0)                (1)

Translation

P'(x, y) = P(x, y) + T(x, y)                      (2)

Where:

If we know that A(x, y) = (1, - 3), B(x, y) = (5, - 1) and C(x, y) = (2, - 5), then the final coordinates are:

Reflection across y-axis

A'(x, y) = (1, - 3) + (- 2, 0)

A'(x, y) = (- 1, - 3)

B'(x, y) = (5, - 1) + (- 10, 0)

B'(x, y) = (- 5, - 1)

C'(x, y) = (2, - 5) + (- 4, 0)

C'(x, y) = (- 2, - 5)

Translation

A''(x, y) = (- 1, - 3) + (4, 5)

A''(x, y) = (3, 2)

B''(x, y) = (- 5, - 1) + (4, 5)

B''(x, y) = (- 1, 4)

C''(x, y) = (- 2, - 5) + (4, 5)

C''(x, y) = (2, 0)

The final coordinates of the triangle are A''(x, y) = (3, 2), B''(x, y) = (- 1, 4) and C''(x, y) = (2, 0), respectively.

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Answer:

z = 14.4

Step-by-step explanation:

RX is an angle bisector and divide the opposite side that are proportional to the other 2 sides , that is

[tex]\frac{SX}{XT}[/tex] = [tex]\frac{RS}{RT}[/tex] ( substitute values )

[tex]\frac{5}{6}[/tex] = [tex]\frac{12}{z}[/tex] ( cross- multiply )

5z = 72 ( divide both sides by 5 )

z = 14.4

Answer:

Again the answer is D

Step-by-step explanation:

For the formula y = 3/8x , as x increases or decreases, the value of y increases or decrease by 3/8 times of x.

We have the following statement -

'The directly proportional dependence is given by the formula y = 3/8x '.

We have to analyze this statement.

Directly proportional means as the value of one variable increases, the value of another variable increases at the same rate.

According to the question, we have -

y = 3/8x

Here -  y is directly proportional to x. This means that as x increases or decreases, the value of y increases or decrease by 3/8 times of x.

The graph of this equation is a straight line passing through origin. Therefore - Direct proportionality is represented by a straight line graphically.

Hence, for the equation y = 3/8x , as x increases or decreases, the value of y increases or decrease by 3/8 times of x.

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the number of pancakes that can be made using the remaining raspberries are 9 pancakes.

We are given that:

Total raspberries = 13 1/4 cups

Total raspberries = 53 / 4 cups

Now, he used 7 / 8 cups to make a smoothie.

So, Raspberries left = 53 / 4 - 7 / 8

Left = 99 / 8 cups

Now, for making 1 pancake Raspberries required = 1 3/8 sups

= 11 / 8 cups

So, the number of pancakes will be calculated by using division:

Number = 99 / 8 ÷ 11 / 8

Number = 99 / 11

Number = 9 pancakes

Therefore, we get that, the number of pancakes that can be made using the remaining raspberries are 9 pancakes.

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Answer:

Only A

Step-by-step explanation:

[tex]b) \: \frac{1}{ {n}^{ - 5} } = {n}^{5} \\ \\ c) \: {n}^{6} \times {n}^{ - 8} = {n}^{ - 2} \\ \\ d) \: {n}^{7} \times {n}^{8} = {n}^{15} \\ \\ e) \: \frac{1}{ {n}^{3} } = {n}^{ - 3} [/tex]

The equation of the line in​ point-slope form is y = -1/3 x + 20/3 and 3y + x = 20

The equation of line perpendicular to another line in point slope form is expressed as;

y-y₁ = -1/m(x-x₁)

Given the equation of a line x -3y - 8 = 0

x - 3y = 8

-3y = -x + 8

y = 1/3x - 8/3

Slope m = 1/3

Substitute the point (-7, 9) and slope 1/3 into the equation

y-9 = -1/3(x-(-7))

y-9 = -1/3(x+7)

3(y-9) = -(x+7)

3y-27 = -x -7

3y = -x + 20

y = -1/3 x + 20/3

Write in general form.

3y = -x + 20

3y + x = 20

Hence the equation of the line in​ point-slope form is y = -1/3 x + 20/3 and 3y + x = 20

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It will take 0.006 seconds for bat's cry to reach its prey and echo back.

Sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid.

Given is the speed of sound which is 330 m/s. The prey is 1 meter away from the bat.

The time it takes a bat's cry to reach its prey and echo back can be calculated using the formula -

time = distance / speed

The distance covered by the sound as it reaches the prey and echo back is equal to 2 x 1 = 2 meters.

Speed of sound → 330 m/s.

So, the time taken will be -

t = 3/330

t = 0.006 s

Therefore, it will take 0.006 seconds for bat's cry to reach its prey and echo back.

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[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &\stackrel{grams}{0.67}\\ t=\textit{elapsed time}\dotfill &\stackrel{years}{460}\\ h=\textit{half-life}\dotfill &\stackrel{years}{92} \end{cases} \\\\\\ A=0.67\left( \frac{1}{2} \right)^{\frac{460}{92}}\implies A=0.67\left( \frac{1}{2} \right)^5\implies A\approx 0.021~grams[/tex]

Answer:

there are 7 shelves. 9 x 7=63

Answer:

the answer is 7 shelves

Step-by-step explanation:

63÷9=7

Answer:

The solution h < 5.5 means that Melanie can rent the bike for no more than 5.5 hours.

Hope this helps :)

Explanation and Check part below.

Step-by-step explanation:

1. Isolate the variable by doing the inverse operation which is in this case subtracting 6 on bothsides of the equation.

8h + 6 < 50

- 6 - 6

8h < 44

2. Dive both sides of the equation by 8.

8h < 44

--- ----- <--------- fraction bar, divide

8 8

h < 5.5

The equation of the line in point-slope form, which passes through the pair of points located at (-4 , 2) and (-3 , 5), is y - 2 = 3(x + 4).

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Getting the slope of the two points: (-4 , 2) and (-3 , 5).

m = (y2 - y1)/(x2 - x1)

m = (5 - 2)/(-3 - -4)

m = 3

Using the point slope form, plug in the values of the slope and Point A to set up the equation.

(y - y1) = m(x - x1)

where m = 3 and (x1 , y1) = (-4 , 2)

(y - 2) = 3(x - -4)

y - 2 = 3(x + 4)

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The number of possible outcomes is 12.

To find the possible outcomes:
Given: 6 colors and 2 seat designs.

Therefore, the number of possible outcomes is 12.

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We have the expression to be written as 2 × 10 =  2 x 10^ 1  = 20

The index form of a number  can be defined as that number written as an exponential expression.

It is also said to be a single number that is  raised to another number.

Given the expression;

2x _____ = 2 x 10^ 1 = ______

It is important to note that a number raised to the power 1 is that same number, so we have;

2 × 10

2 x 10^1 = 2 × 10

2 × 10  = 20

Thus, we have the expression to be written as 2 × 10 =  2 x 10^ 1  = 20

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The solution of the given equation 3/b+2 = 6/b-1 is found to be (y = -5).

The numerator of the 1st fraction is multiplied by denominator of the 2nd fraction, and the numerator of the 2nd fraction is multiplied by denominator of the 1st fraction in cross-multiplication.

Now, for the given equation in the question;

3/b+2 = 6/b-1

Cross multiplying the terms;

3(b - 1) = 6(b + 2)

Opening the brackets;

3b - 3 = 6b + 12

Bring the variables and constants on the different sides.

6b - 3b  = -3 - 12

3b = -15

b = -5

Therefore, the solution of the stated equation 3/b+2 = 6/b-1 is found to be (b = -5).

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x = 345.54545454 is  the value of x to the nearest tenth. 1086/π = x

What is π ?

Why is pi so important?

1086/π = x

Put value of π = 22/7

1086/22/7 = x

x = 49.363636 × 7

x = 345.54545454

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Answer:

GCF of numbers 24, 40, 60 is 4

GCF(24, 40, 60) = 4

Answer:8.75

Step-by-step explanation:

3/4=0.75

0.75+8=8.75

Main Answer:

c. The value of x = 5 and y = 5.

d. The value of x = 1and y = 2.

e. The value of x = 10 and y = 2.

f. The value of x = 2 and y = 1.

g. The value of x=2 and y = 4.

Explanation for all parts:

c.  Given: 3y = x + 10

               [tex]x^{2} +y^{2}=100[/tex]

    To find: Solve the simultaneous equations.

    [tex]x^{2} +y^{2}=100[/tex]

    On taking square root from both sides of the equations, we get,

     x + y = 10

     3y = x + 10

     x = 3y - 10

     x - 3y = -10

     By elimination method,

     x - 3y = -10

     x + y  = 10

     -----------------

         -4y = -20

            y = 5

    On substituting the value of y = 5 in the equation x + y = 10 , we get,

    x + y =10

    x + 5 = 10

    x = 5

   Therefore, the required value of x = 5 and y = 5.

d.  Given: y = 3x - 1

               8[tex]x^{2}[/tex] - 2xy = 4

     To find: Solve the simultaneous equations.

     By substitution method,

     We will substitute the value of y in equation 8[tex]x^{2}[/tex] - 2xy = 4 to get,

      8[tex]x^{2}[/tex] - 2x(3x-1) = 4

      8[tex]x^{2}[/tex] - 6[tex]x^{2}[/tex] +2x = 4

      2[tex]x^{2}[/tex] + 2x = 4

      By dividing the equation by 2 on both sides, we get,

       [tex]x^{2}[/tex] + x = 2

       [tex]x^{2}[/tex] + x - 2 = 0

       [tex]x^{2}[/tex] + 2x - x - 2 = 0

       x(x+2) -1(x+2) = 0

       (x+2)(x-1) = 0

       x+2 = 0 or x - 1= 0

       x = -2 or x = 1

       We will not consider the negative values of x.

       So, x = 1.

       y= 3x - 1

       y = 3 × 1- 1

       y = 3 - 1

       y = 2  

       The value of x = 1and y = 2..

e. Given: x - 2y = 6

              [tex]x^{2}[/tex] - 4xy = 20

  To find: Solve the simultaneous equations

     x - 2y = 6

     x= 6 + 2y

     By substitution method,

     We will substitute the value of x= 6 + 2y in the equation  

      [tex]x^{2}[/tex] - 4xy = 20 to get,

     [tex](6+2y)^{2}[/tex] - 4(6+2y)y = 20

      36 + 4[tex]y^{2}[/tex] +24y - 24y - 8[tex]y^{2}[/tex] = 20

      -4[tex]y^{2}[/tex] = 20 - 36

       -4[tex]y^{2}[/tex]  = -16

       By dividing the equation by -4 on both sides, we get,

        [tex]y^{2}[/tex] = 4

        y = 2

       So, x = 6 +2y

             x = 6 + 2×2

             x = 6+4

             x=10

       Therefore, the value of x = 10and y = 2.

f. Given: 4x - 3y = 5

              [tex]x^{2} +3xy = 10[/tex]

  To find: Solve the simultaneous equations.

  4x - 3y = 5

   4x= 5 + 3y

   x = [tex]\frac{5+3y}{4}[/tex]

  By substitution method,

  We will substitute the value of x = [tex]\frac{5+3y}{4}[/tex] in the equation

        [tex]x^{2} +3xy = 10[/tex] to get,

   [tex](\frac{5+3y}{4} )^{2}[/tex] + 3[tex](\frac{5+3y}{4} )[/tex]y =10

    [tex]\frac{25+9y^{2}+30y }{16}+ \frac{15y+9y^{2} }{4}[/tex] = 10

    [tex]\frac{25+9y^{2}+30y+60y+36y^{2} }{16}[/tex]=10

    25 + 45[tex]y^{2}[/tex] + 90y=160

  By dividing the equation by 5 on both sides, we get,

    5 + 9[tex]y^{2}[/tex] +18y= 32

     [tex]9y^{2}[/tex] +18y - 27 = 0

   By dividing the equation by 3 into both sides, we get,

    [tex]y^{2}[/tex] +2y - 3 = 0

    [tex]y^{2}[/tex] +3y -y - 3 = 0

    y(y+3) - 1(y+3) = 0

     (y+3)(y-1) = 0

     y =-3 or y =1

     We will not consider the negative values of x.

     So, y=1.

     x= [tex]\frac{5+3y}{4}[/tex]

     x = [tex]\frac{5+3(1)}{4}[/tex]

    x= [tex]\frac{5+3}{4}[/tex]

    x= [tex]\frac{8}{4}[/tex]

    x = 2

Therefore, the value of x=2 and y= 1.

g. Given: 2x+ y= 8

               xy= 8

   To find: Solve the simultaneous equations.

According to the equation,

    2x+ y= 8

    y = 8 - 2x

By substitution method,

  We will substitute the value of y = 8 - 2x in the equation xy = 8 to get,

x(8-2x) = 8

8x - 2[tex]x^{2}[/tex] = 8

8x - 8 = 2[tex]x^{2}[/tex]

2[tex]x^{2}[/tex] - 8x + 8 = 0

2[tex]x^{2}[/tex] - 4x - 4x + 8 =0

2x(x - 2) - 4(x - 2) = 0

(x - 2)(2x - 4) = 0

x = 2 or 2x = 4

x= 2 or x =2

So, y = 8 - 2x

     y = 8 - 2(2)

     y = 8 - 4

    y = 4

Therefore, the value of x = 2 and y= 4.

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Answer:

569,75

Step-by-step explanation: